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Mathematics Grades 6-12

Mathematics Grades 6-12. February NTI February 4, 2013. Overview of the Day. Standards for Mathematical Practice Progressions Documents - Grades 6-8 & 9-12 NYSED Assessment Development Lunch 4a. LearnZillion – Grades 6-8 4b. PARCC Model Content Frameworks -

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Mathematics Grades 6-12

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  1. MathematicsGrades 6-12 February NTI February 4, 2013 EngageNY.org

  2. Overview of the Day • Standards for Mathematical Practice • Progressions Documents - Grades 6-8 & 9-12 • NYSED Assessment Development Lunch 4a. LearnZillion – Grades 6-8 4b. PARCC Model Content Frameworks - Grades 9-12 EngageNY.org

  3. Objectives Gain a deeper understanding of the eight Standards for Mathematical Practice, articulate them to others, and implement the MPs in the classroom alongside mathematical content standards. Identify key areas to focus on in the areas of Ratio and Proportional Relationships ( Grades 6 and 7) and Functions (Grades 8-12). Become familiar with the PARCC Model Content Frameworks and compare similarities and differences between the PARCC MCF and CCSSM Appendix A. EngageNY.org

  4. “The formulation of the problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill.” -Albert Einstein EngageNY.org

  5. Standards for Mathematical Practice GRADES 6-12 Teri Calabrese-Gray, CVES Assistant Superintendent EngageNY.org

  6. Standards for Mathematical Practice “Chairs in Hall” – Illustrative Mathematics Three hallways contained 9,876 chairs altogether. One-fifth of the chairs were transferred from the first hall to the second hall. Then, one-third of the chairs were transferred from the second hall to the third hall and the number of chairs in the third hall doubled. In the end, the number of chairs in the three halls became the same. How many chairs were in the second hall to begin with? EngageNY.org

  7. Standards for Mathematical Practice The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years. Designers of curricula, assessments, and professional development should all attend to the need to connect the mathematical practices to mathematical content in mathematics instruction. EngageNY.org

  8. Standards for Mathematical Practice The Standards for Mathematical Content are a balanced combination of procedure and understanding. Expectations that begin with the word “understand” are often especially good opportunities to connect the practices to the content. Students who lack understanding of a topic may rely on procedures too heavily. EngageNY.org

  9. Standards for Mathematical Practice Without a flexible base from which to work, students may be less likely to consider analogous problems, represent problems coherently, justify conclusions, apply the mathematics to practical situations, use technology mindfully to work with the mathematics, explain the mathematics accurately to other students, step back for an overview, or deviate from a known procedure to find a shortcut. EngageNY.org

  10. Standards for Mathematical Practice In this respect, those content standards which set an expectation of understanding are potential “points of intersection” between the Standards for Mathematical Content and the Standards for Mathematical Practice. These points of intersection are intended to be weighted toward central and generative concepts in the school mathematics curriculum that most merit the time, resources, innovative energies, and focus necessary to qualitatively improve the curriculum, instruction, assessment, professional development, and student achievement in mathematics. EngageNY.org

  11. Standards for Mathematical Practice • Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. EngageNY.org

  12. Standards for Mathematical Practice ACTIVITY Using the Standards for Mathematical Practice (MP) handout on your table and the number you selected for your table, please read the corresponding MP. Divide your piece of chart paper in half and on one side label it Student Evidence and on the other side label it Teacher Evidence. Don’t forget to write the number of the MP you selected on your chart paper as well. EngageNY.org

  13. Standards for Mathematical Practice ACTIVITY (cont’d) Brainstorm with members at your table what students would be doing in the classroom if this MP was being implemented effectively and list evidence on your chart paper. Next, brainstorm with members at your table what teachers would be doing in the classroom if this MP was being implemented effectively and list evidence on your chart paper. EngageNY.org

  14. Standards for Mathematical Practice ACTIVITY (cont’d) Locate all those tables that worked on the same MP as you and come together as one group and share your work. Review the evidence and determine if it should stay on the chart or be deleted. Be prepared to report out. EngageNY.org

  15. Standards for Mathematical Practice EngageNY.org MP 1: Make sense of problems and persevere in solving them.

  16. Standards for Mathematical Practice MP 2: Reason abstractly and quantitatively. EngageNY.org

  17. Standards for Mathematical Practice MP 3: Construct viable arguments and critique the reasoning of others. EngageNY.org

  18. Standards for Mathematical Practice MP 4: Model with mathematics. EngageNY.org

  19. Standards for Mathematical Practice MP 5: Use appropriate tools strategically. EngageNY.org

  20. Standards for Mathematical Practice MP 6: Attend to precision. EngageNY.org

  21. Standards for Mathematical Practice MP 7: Look for and make use of structure. EngageNY.org

  22. Standards for Mathematical Practice MP 8: Look for and express regularity in repeated reasoning. EngageNY.org

  23. Standards for Mathematical Practice PROBLEM What is the mean of 5, 8, 9, and 6? EngageNY.org

  24. Standards for Mathematical Practice Identify the MPs that align with this problem. Discuss at your tables. EngageNY.org

  25. Standards for Mathematical Practice Pose a different problem that could go deeper but require the same mathematical content knowledge? EngageNY.org

  26. Standards for Mathematical Practice Explain what students might learn from the second question compared to the first question? EngageNY.org

  27. Standards for Mathematical Practice Explain what a teacher might learn from how students answer the first question compared to how students answer the second question? EngageNY.org

  28. Integrating the Standards for Mathematical Practice Inside +=x Mathematics Watch the video using the Inside Mathematics link above and collect evidence from the lesson that exemplifies the Standards for Mathematical Practice. Focus on both the students and the teacher. EngageNY.org

  29. Integrating the Standards for Mathematical Practice Inside +=x Mathematics Compare your evidence with an elbow partner and then engage in a conversation with members at your table to come to consensus as to which MPs you observed. EngageNY.org

  30. Integrating the Standards for Mathematical Practice Inside +=x Mathematics For a more in-depth study of the Standards for Mathematical Practice, please visit http://www.insidemathematics.org/index.php/commmon-core-math-intro. EngageNY.org

  31. Standards for Mathematical Practice MP Placemat Activity Everyone will need the MP Placemat and the MP Activity Cards. Read through the MP Activity Cards on your own. Once you have read the activity cards, you need to decide where you would put them on your placemat. You have 16 activity cards and 16 boxes on your placemat. EngageNY.org

  32. Standards for Mathematical Practice MP Placemat Activity(cont’d) First you will have time to work independently and then in small groups at your table. In the end, your table must come to consensus and a representative needs to come up and post their results on the master placemat. EngageNY.org

  33. Common Core State Standards: Progressions GRADES 6-12 Kristine S. Cole, SUNY Research Fund Fellow Teri Calabrese-Gray, CVES Assistant Superintendent EngageNY.org

  34. Common Core State Standards: Progressions Let’s look at Grades 6-7, Ratios and Proportional Relationships and how it builds to Grade 8 , High School, Functions EngageNY.org

  35. Common Core State Standards: Progressions K-W-L EngageNY.org

  36. Common Core State Standards: Progressions The Common Core State Standards in mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels, informed both by research on children's cognitive development and by the logical structure of mathematics. These documents were spliced together and then sliced into grade level standards. EngageNY.org

  37. Common Core State Standards: Progressions This would be useful in teacher preparation and professional development, organizing curriculum, and writing textbooks. Progressions documents also provide a transmission mechanism between mathematics education research and standards. Research about learning progressions produces knowledge which can be transmitted through the progressions document to the standards revision process; questions and demands on standards writing can be transmitted back the other way into research questions. EngageNY.org

  38. Common Core State Standards: Progressions From that point on the work focused on refining and revising the grade level standards. The early drafts of the progressions documents no longer correspond to the current state of the standards. The progressions can explain why standards are sequenced the way they are, point out cognitive difficulties and pedagogical solutions, and give more detail on particularly knotty areas of the mathematics. EngageNY.org

  39. Common Core State Standards: Progressions Grades 6-7 – Ratios and Proportional Relationships Grade 8 and High School – Functions EngageNY.org

  40. Common Core State Standards: Progressions Grades 6-7 Ratios and Proportional Relationships • Overview – Pages 2-4 • Grade 6 – Pages 5-7 • Grade 7 – Pages 8-12 EngageNY.org

  41. Common Core State Standards: Progressions Grade 8 and High School: Functions • Overview and Grade 8 – Pages 2-6 • Battery Charging – Page 5 • High School – Interpreting Functions – Pages 7-10 • Interpreting the Graph – Page 7 • Cell Phones – Page 8 • Warming and Cooling – Page 9 EngageNY.org

  42. Common Core State Standards: Progressions Grade 8 and High School Functions • High School – Building Functions – Pages 11-13 (stop before advanced standards) • Lake Algae – Page 11 • Transforming Functions – Page 12 • High School – Linear and Exponential Models – Pages 15-16 EngageNY.org

  43. Common Core State Standards: Progressions ACTIVITY Each group is responsible for their respective sections of the Progressions documents. Once your table has read their section of the document and engaged in an initial discussion, locate similar tables who read the same section. EngageNY.org

  44. Common Core State Standards: Progressions ACTIVITY (cont’d) The goal of the activity is to use the collective knowledge of your group to develop a unique way to present your material to the entire group. Once everyone has completed their work, they will be asked to report out. EngageNY.org

  45. Common Core State Standards: Progressions Grades 6-7 Ratios and Proportional Relationships • Grade 6 • Grade 7 • Overview EngageNY.org

  46. Common Core State Standards: Progressions Grade 8 and High School: Functions • Grade 8 • High School – Interpreting Functions • High School – Building Functions • High School – Linear and Exponential Models • Overview EngageNY.org

  47. Common Core State Standards: Progressions Influenza Epidemic http://www.illustrativemathematics.org/illustrations/637 EngageNY.org

  48. Common Core State Standards: Progressions (Task from Functions Modeling Change: A Preparation for Calculus, Connally et al., Wiley 2010.) An epidemic of influenza spreads through a city. The figure below is the graph of I=f(w) , where I is the number of individuals (in thousands) infected w weeks after the epidemic begins. EngageNY.org

  49. Common Core State Standards: Progressions • Estimate f(2) and explain its meaning in terms of the epidemic. • Approximately how many people were infected at the height of the epidemic? When did that occur? Write your answer in the form f(a)=b . (Task from Functions Modeling Change: A Preparation for Calculus, Connally et al., Wiley 2010.) EngageNY.org

  50. Common Core State Standards: Progressions EngageNY.org

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